Or one could just go to Morthal and find him themselves. He's kinda hard to miss.
I believe you have to speak to an inn keeper though to start the misc objective to go the Falion. I think if do not speak to the inn keeper, and go straight to Falion, you will not have a dialogue option about curing your vampirism. Though, I do not know from personal experience, as I am a Werewolf, but from what I have read on the forums and wiki, you have to speak to an inn keeper.